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New paper

Implementation of holonomic quantum computation through engineering and manipulating environment

Zhang-qi Yin, Fu-li Li and Peng Peng

We consider an atom-field coupled system, in which two multilevel atoms are respectively trapped in two distant cavities which are connected by an optical fiber and are shined by a broadband squeezed light. We show that a two-qubit geometric CPHASE gate between the two atoms can be implemented through adiabatically manipulating the squeezed reservoir along a closed loop. The scheme has two remarkable features. First, no matter how small but nonzero the squeezing amplitude is, a CPHASE gate with arbitrary phase shift can always be implemented. Second, in contrast to previous quantum computation schemes, the larger the effective coupling strength between the environment and the atoms is, the more reliable the realized CPHASE gate is.

In this work, we investigate the possiblility of realizing quantum computation via steering environment, other than controlling Hamiltonian of the quantum systems themselves or choosing measurement strategy. Let me briefly explain our motivation on doing this work.

When building future quantum computer, we must investigate practical systems which could be divided into three subsystems, which are quantum systems, quantum environments and detectors. Up to now, to our knowledge, there are two different types of schemes, controlling the Hamiltonian of quantum systems themselves (see Cirac and Zoller’s paper in 1995) and choosing measurement strategy (such as one-way quantum computer). So it would be interesting to investigate whether it is possible to realize quantum logic gate, such as a two-qubit CPHASE gate, via manipulating quantum environment. Our work reveals this possibility. Therefore, combining our resualts with previous works, we get following insights: Hamiltonians of the quantum systems, environment where quantum systems place and detectors which measure quantum systems, each of them could be manipulated to realize quantum compution.

I believe this work makes our understanding on realizing quantum computation and quantum control more deeply. In doing this work, we got valueable suggestions from Xiao Yun-feng (USTC). I also thank Star Forum where I got valueable suggestions.